You roll a number cube numbered one to six 12 times. P(5) = two over three. What type of probability is illustrated and why? (1 point)
experimental; the result is based on the number of possible outcomes
** experimental; the result is found by repeating an experiment
theoretical; the result is based on the number of possible outcomes
theoretical; the result is found by repeating an experiment
2. You draw five cards from a standard deck of 52 cards. P(heart) = 4 over 5. What type of probability is illustrated and why? (1 point)
theoretical; the result is based on the number of possible outcomes
theoretical; the result is found by repeating an experiment
experimental; the result is based on the number of possible outcomes
** experimental; the result is found by repeating an experiment
3. A number cube is rolled 150 times. The number 3 comes up 43 times. What is the experimental probability of rolling a 3? What is the theoretical probability of rolling a 3? (1 point)
forty three over one hundred fifty ; one sixth
forty three over one hundred fifty ; one over fifty
one sixth ; forty three over one hundred fifty
three over forty three ; one sixth
4. A spinner is divided into 11 equal sections numbered from 0 to 10. You spin the spinner once. What is P(not even)? (1 point)
three fifths
one half
five over eleven**
six over eleven
5. A bag contains 9 green marbles and 11 white marbles. You select a marble at random. What are the odds in favor of picking a green marble? (1 point)
9:20
2:9
11:9
9:11***
6. Food Express is running a special promotion in which customers can win a free gallon of milk with their food purchase if there is a star on their receipt. So far, 129 of the first 138 customers have not received a star on their receipts. What is the experimental probability of winning a free gallon of milk? (1 point)
3 over 46**
43 over 46
11 over 138
43 over 138
7. A bag contains 7 green marbles, 9 red marbles, 10 orange marbles, 5 brown marbles, and 10 blue marbles. You choose a marble, replace it, and choose again. What is P(red, then blue)? (1 point)
seventy-seven over one hundred sixty-four
** nineteen over forty-one
ninety over one thousand six hundred eighty-one
forty-five over forty-one
8. Each of two urns contains green balls and red balls. Urn I contains 10 green balls and 8 red balls. Urn II contains 3 green balls and 10 red balls. If a ball is drawn from each urn, what is P(red and red)? (1 point)
twenty-three over eighteen
ten over twenty-seven
forty over one hundred seventeen
*** eighteen over thirty-one
9. If you spin the spinner below twice, what is P(vowel, then Q)?
counter (1 point)
one-tenth
one-ninth **
two-ninths
one-twelfth
10. You have four $1 bills, two $5 bills, five $10 bills, and five $20 bills in your wallet. You select a bill at random. Without replacing the bill, you choose a second bill. What is P($1, then $10)? (1 point)
nine over thirty-nine**
five over sixty-four
three over eighty
one-twelfth
11. A basket contains the following pieces of fruit: 3 apples, 2 oranges, 2 bananas, 2 pears, and 5 peaches. Jack picks a fruit at random and does not replace it. Then Bethany picks a fruit at random. What is the probability that Jack gets a peach and Bethany gets an orange? (1 point)
10 over 27
5 over 91**
5 over 98
93 over 182
12. The probability of a basketball player hitting a foul shot is one-third. How many shots would you expect her to make in 90 attempts? (1 point)
30**
60
3
45
13. A true-false test has 12 questions. What is the probability of guessing the correct answers to all of the questions? (1 point)
1 over 4096
1 over 144
one over twenty four**
1over14
14. Simplify 4! (1 point)
24**
10
9
4
15. Simplify 6P2. (1 point)
30**
15
12
720
16. Simplify 9C4. (1 point)
126**
15,120
5
3,024
17. You and 3 friends go to a concert. In how many different ways can you sit in the assigned seats? (1 point)
6 ways**
12 ways
24 ways
10 ways
18. You own 6 pairs of jeans and want to take 2 of them with you on vacation. In how many ways can you choose 2 pairs of jeans? (1 point)
10
12
15
20
We do not do your homework for you. Although it might take more effort to do the work on your own, you will profit more from your effort. We will be happy to evaluate your work though.
However, just as a start, I disagree with your first answer.
Also, "five over eleven" can be written most easily as 5/11. Use that for your other fractions.
we are not here looking for the answers, we are checking our answers
1. The probability illustrated in this scenario is experimental probability. Experimental probability is based on the result of repeating an experiment. In this case, rolling a number cube 12 times and obtaining a 5 two-thirds of the time. By conducting the experiment multiple times, we can determine the probability based on the observed outcomes.
2. The probability illustrated in this scenario is theoretical probability. Theoretical probability is based on the number of possible outcomes. In this case, drawing five cards from a standard deck of 52 cards and obtaining a heart four-fifths of the time. The probability is based on the assumption that all the cards have an equal chance of being drawn.
3. The experimental probability of rolling a 3 is 43/150. This is found by dividing the number of times a 3 came up (43) by the total number of times the number cube was rolled (150).
The theoretical probability of rolling a 3 is 1/6. This is based on the fact that there is only one 3 on the number cube out of six possible numbers.
4. The probability of rolling a not even number on the spinner is 5/11. This can be calculated by counting the number of odd numbers on the spinner (6) and dividing it by the total number of sections on the spinner (11).
5. The odds in favor of picking a green marble are 9:11. This is calculated by dividing the number of green marbles (9) by the total number of marbles (9 + 11 = 20).
6. The experimental probability of winning a free gallon of milk is 3/46. This is found by dividing the number of customers who have not received a star on their receipts (129) by the total number of customers (138).
7. The probability of selecting a red marble and then a blue marble is 19/41. This is calculated by multiplying the probability of selecting a red marble (9/41) by the probability of selecting a blue marble after replacing the first marble (10/41).
8. The probability of drawing a red ball from each urn is 18/31. This is calculated by multiplying the probability of drawing a red ball from Urn I (8/18) by the probability of drawing a red ball from Urn II (10/13).
9. The probability of spinning a vowel and then a Q is 1/9. This is found by multiplying the probability of spinning a vowel (2/10 = 1/5) by the probability of spinning a Q after replacing the first spin (1/9).
10. The probability of selecting a $1 bill and then a $10 bill is 9/39. This is calculated by multiplying the probability of selecting a $1 bill (4/16 = 1/4) by the probability of selecting a $10 bill after not replacing the first bill (5/19).
11. The probability of Jack getting a peach and Bethany getting an orange is 5/91. This is calculated by multiplying the probability of Jack getting a peach (5/14) by the probability of Bethany getting an orange after not replacing Jack's pick (2/13).
12. The probability of the basketball player hitting a foul shot is 1/3. In 90 attempts, we can expect her to make approximately 30 shots. This is found by multiplying the probability (1/3) by the number of attempts (90).
13. The probability of guessing the correct answers to all 12 questions on the true-false test is 1/4096. This is calculated by multiplying the probability of guessing each question correctly (1/2) twelve times.
14. 4! (4 factorial) is equal to 24. This is calculated by multiplying 4 by its preceding numbers (4 x 3 x 2 x 1).
15. 6P2 (6 permutation 2) is equal to 30. This is calculated by multiplying 6 by 5.
16. 9C4 (9 combination 4) is equal to 126. This is calculated using the combination formula, which is equal to n! / (r! * (n-r)!), where n is the number of objects to choose from and r is the number of objects to choose.
17. The number of different ways you can sit in the assigned seats with 3 friends at a concert is 6 ways. This is calculated using the formula for permutations, which is n! / (n-r)!, where n is the total number of people and r is the number of friends.
18. The number of ways you can choose 2 pairs of jeans out of 6 pairs is 15 ways. This is calculated using the formula for combinations, which is n! / (r! * (n-r)!), where n is the total number of options and r is the number of options to select.